Preheat your oven to 375°F. Wash your stone fruit under cool water and pat dry—this keeps the filling from getting too watery. Slice each fruit into quarter-inch pieces and remove the pit (yes, tedious, but trust me on this). Toss the sliced fruit in an 8-by-10-inch baking dish with both sugars, lemon juice, cinnamon, and nutmeg.
Mix the fruit filling gently with your hands so everything's coated but you're not crushing the fruit pieces. Let it sit while you make the topping—this lets the sugar start dissolving and the juices get released. The filling might look dry now, but it'll bubble up beautifully during baking.
In a separate bowl, combine rolled oats, flour, salt, and a tiny squeeze of lemon zest if you've got it. Grab that melted butter and pour it over the oat mixture, stirring with a fork until everything gets all clumpy and cohesive. This is the textural magic happening—don't rush it.
Fold in your chopped almonds and pecans, breaking apart any big clumps with your fingers. The mixture should look kinda crumbly and feel like wet sand. If it seems too dry, add another tablespoon of melted butter and keep going—every oven's humidity is different, so adjust as needed.
Spread the topping over your fruit filling, leaving maybe a quarter-inch around the edges so you can see the fruit bubbling. Don't pack it down—you want it to stay loose and crispy, not cement itself into one solid block (I learned this the hard way my first time making this crisp).
Bake for 35 to 40 minutes until the topping turns golden brown and the filling starts bubbling at the edges. Your kitchen smells absolutely amazing when it gets to about minute 25, and that's your signal you're getting close. Careful not to overbake or the topping gets hard instead of crispy.
Let it cool for 10 to 15 minutes before serving—this gives it structure so it doesn't fall apart on your plate. The summer stone fruit crisp thickens as it cools and becomes even better. Serve warm with whatever topping you've got on hand.